Comparison & Discussion of Secondary Electron Emission (SEE) Materials - Theory

1. Comparison & Discussion of Secondary Electron Emission (SEE) Materials - Theory Z.Insepov, V. Ivanov, S. Jokela

2. Outline Simulation chart SEE Yields for various materials Future SEE tasks Charge relaxation time Future simulation plans Summary

3. Simulation work chart Micro-scopic SEE, PE Saturation Heating & Aging simulations SEE = f(E) SEE = g(q) t – relax. time Materials properties Relaxation times SEE, PE Escape length Mater. properties MCP Experiments T = f(z) Materials properties Gain, Rt Macro-scopic Gain, Rt, saturation simulations Macroscopic Fringe-field Comsol simulations Map of electric fringe field Relaxation times

4. q f Low-Energy Monte Carlo codes Casino simulation Inelastic, Bethe-Joy (1989) • Algorithm of SEE calculations Berger-Seltzer (1970) Elastic, Rutherford J– the mean ionization potential e – energy for production of SE l – mean free path, escape length a - screening factor e = 20 eV l = 60 Å Al2O3, D. Joy (1995) Insulators, Kanaya (1978)

5. SEE yield calculation via MC Monte Carlo algorithm • Initial electrons are created, E = 0.1 - 4 keV, q = 0-89 • New electron, new trajectory, similar to previous • The process continued until the electron E < E0 • 1-10K trajectories computed for each sample (error  1/N) • h=102-104 Å samples were simulated (100Å - 1 mm) Experimental data from literature • Experimental SEE yields were compared with our calculations

6. SEE Yield calculations • MgO • Al2O3 • ZnO • Copper • Gold • Molybdenum Nel=103-104 E, ev q SEE h Target

7. Simulation Group paper • Z. Insepov, V. Ivanov, H. Frisch, Comparison of Candidate Secondary Electron Emission Materials (accepted for publication in NIMB)

8. Why Monte-Carlo ? Empirical, semi-empirical SEE Models are too bad • Specific material, bulk, flat surface, one element, no angular dependence Monte Carlo simulation algorithm is simple • Search for high SEE materials -- Gain/TTS critical to SEE at first strike • Higher QE PC for thin films, ML, nanostructured coatings • Mixture of materials (Alumina+ZnO) • Surface roughness can be studied • Materials aware MCP simulation – against blind experimentation Experimental data from literature are not good • SEE for E-dependence, no angular Experimental data at Argonne • ANL characterization experiments are in progress

9. e, q Empirical Models • No space charge effect, no surface charging effect • Poisson distribution for the SEE • Maxwellian energy and Cosine angular distributions • Bulk material, flat surface, no temperature effects • Ito (1984) • Yakobson (1966) • Guest (1971) b – adjustable parameter • Agarwal (1958)

10. Comparison of SEE- models

11. Alumina SEE Yield: MC vs Experiment

12. ZnO SEE Yields: MC vs Experiment

13. Metal SEE Yields: MC vs Experiment

14. MgO SEE Yields: MC vs Experiment

15. MgO SEE Yield vs q (E-different)

16. Charge relaxation time

17. Analytical model of saturation effects E0z, M0 – electric field and a gain for non-saturated mode I0 – initial current of photo electrons, IR – resistance current τ– relaxation time for induced positive charges [Berkin et al, Tech. Phys. Lett.(2007) 75] Electric field Gain Shape function

18. AZO Maxwell relaxation times

19. Primary electron z SEE r = 10 nm Al2O3+ZnO r z Dr r DD-Model of charge relaxation A. Spherical symmetry B. Cylindrical symmetry r = 20 mm Dr= 10 nm Aspect ratio 40 Da – diffusion coefficient, ma - mobility, na - density of carriers (a = e, h) [1] A.K. Jonscher, Principles of semiconductor device operations, Wiley (1960). [2] A.H. Marshak, Proc. IEEE 72, 148-164 (1984). [3] A.G. Chynoweth, J. Appl. Phys. 31, 1161-1165 (1960). [4] R. Van Overstraeten, Solid St. Electronics 13 (1970) 583-608. [5] L.M. Biberman, Proc. IEEE 59, 555-572 (1972). [6] Z. Insepov et al, Phys.Rev. A (2008) [7] I. Costina et al, Appl. Phys. Lett.78 (2001)

20. Input parameters for DDM • Diffusion coefficients of amorphous alumina are unknown • Carrier mobilities for alumina are known for limited mixture content • ZnO with 1% of Al2O3 was measured: m=40 cm2/Vs, r=1.410−4(cm) [1] • Conductivity of AZO with 20% Al: r = 107 ( cm), mobility unknown. • Assuming linear dependence between conductivity and mobility, mobility of a mixture Al2O3+ZnO was extrapolated from low Al-content to high. • Diffusion coefficients via Einstein relation: D = mkBT/e. [1] Ruske, Electrical transport in Al-doped zinc oxide, J. Appl. Phys. (2010).

21. Proposed material constants • Mobility and diffusion constants of carriers were extrapolated from low Al-content to high [1] SiO2, Dapor [Dapor, Surf. Interface Anal. 26, 531È533 (1998)]

22. Charge dissipation in Al2O3+ZnO Set of equations for the drift-diffusion model were numerically solved for several values of material constraints and the relaxation times were obtained.

23. Internal Electric field

24. Hole densities vs time, Al2O3+ZnO • Variable – diffusion coefficients, Dh Dh=1.2e-11 cm2/s Dh=1.2e-10 cm2/s Dh=1.2e-8 cm2/s Dh=1.2e-9 cm2/s

25. Relaxation times via DDM • Relaxation time vs diffusion coefficients Dh=1.2x10-11 cm2/s Dh=1.2x10-10 cm2/s Dh=1.2x10-8 cm2/s SiO2, Dapor (1998) Maxwell relaxation time

26. Status of relaxation time Experimental verification of relaxation time model – under progress (APS/HEP) Our calculations will be extended to electrons and two types of holes – to be compared to Auger Different local nano-structures of the mixture Two types of geometries: plane and cylindrical Ambipolar drift-diffusion model is essential Relaxation time is obtained via numerical solution of the kinetics of charge carriers Impact ionization model will be added

27. Relaxation time measurement • Continuous delay within 5m (15 ns) • Laser flashing (Ed May) – 1 ms B. Adams

28. Future simulation work Photo-electron bunch formation • Microscopic model of the photo-electron emission (Zeke, Klaus, Bernard); • Angular and energy distribution for the photo-emitted electrons (Zeke); • Bunch formation for electron optical calculations (Valentin); Saturation effects • Systematic study the charge relaxation time vs. the material properties (Zeke); • Continue study how saturation phenomena affect on the gain & time resolution for real devices, comparison the simulations and experiment (Valentin). Heating effects Aging effects Roughness effects Mixing and multilayer effects